UG : TRB - MATHS - UNIT - 1 - IMPORTANT TOPIC - HYPERBOLIC FUNCTION

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UNIT – 1

1. POLYNOMIALEQUATIONS – IMAGINARY AND IRRATIONALROOTS – RELATION BETWEEN ROOTS AND COEFFICIENTS – SYMMETRIC FUNCTION OF ROOTS IN TERMS OF COEFFICIENT

2. TRANSFORMOFEQUATION – RECIPROCAL EQUATION – INCREASE AND DECREASE THE ROOTS OF GIVEN EQUATION REMOVAL OF TERMS – DESCARTE’S RULE OF SIGNS – APPROXIMATE SOLUTION OF ROOTS OF POLYNOMIAL BY HORNER’S METHOD – CARDAN’S METHOD OF SOLUTION OF CUBIC POLYNOMIAL

3. SUMMATION OFSERIESUSINGBINOMIAL – EXPONENTIAL AND LOGARITHMIC SERIES

4.SYMMETRIC – SKEW SYMMETRIC, HERMITIAN – SKEW HERMITIAN, ORTHOGONAL MATRICES, UNITARY MATRICES EIGEN VALUES – EIGEN VECTORS – CAYLEY HAMILTON THEOREM – SIMILAR MATRICES – DIAGONALIZATION OF MATRICES

5.DECOMPOSITION OF A COMPOSITE NUMBER AS A PRODUCT OF PRIMES UNIQUELY – EULER FUNCTION CONGRUENCE MODULO n, HIGHEST POWER OF PRIME NUMBER P CONTAINED IN n – PRIME AND COMPOSITE NUMBERS – EULER’S FUNCTION – CONGRUENCES - FERMAT’S, WILSON’S AND LAGRANGE’S THEOREM

6. EXPANSIONS OF POWER OF SINNX, COSNX, TANNX – SUMMATION BY CTIS METHOD, TELESCOPIC SUMMATION

7. EXPANSION OF SINX, COSX, TANX IN TERMS OF x– SUM OF ROOTS OF TRIGONOMETRIC EQUATION, FORMATION OF EQUATION WITH TRIGONOMETRIC ROOTS

8.HYPERBOLIC FUNCTIONS –RELATIONBETWEEN CIRCULAR AND HYPERBOLIC FUNCTION – INVERSE HYPERBOLIC PRINCIPAL AND GENERAL VALUES

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